Non-functioning remotes

For the last several months our remotes don't work well (or sometimes at all) with the DVR.  There have been no changes during that time which would require us to make any changes such as pairing a new device or new equipment.  We have an X1 DVR and the smaller converter box (don't know what it's actually called).  Neither remote works with either of the Xfinity devices.  What happens is we can turn the tv on but then if you try to go to the guide, switch channels, on demand, saved programming - anything, you can't do anything.  The remote doesn't light up like the batteries are dead but there are literally brand new batteries in the remotes.  If i push down on the buttons hard enough they will EVENTUALLY start working but very slowly.  So if I try to watch a recorded show and fast forward through the commercials, there's a huge hesitation and then it MIGHT start to slowly fast forward but I usually can't get it up to the 4x speed.  I'm thinking our equipment is so old that the devices and remotes just aren't functioning any longer.  I've contacted Xfinity support twice concerning this and they just want to send a refresh signal to the DVR.  They don't seem to understand that's not the problem.  It seems to be more of a compatability issue.

Anyone else have this issue or know how to remedy it?